Question

if alpha and beta are the zeros of the quadratic polynomial 5 x square + 2 x minus 1 then write the values of alpha + beta

Answer 1

Given,

Quadratic Polynomial = 5x² + 2x - 1.

Zeroes are α and ß.

As α and ß are its zeroes, so

⇒ 5x² + 2x - 1 = k ( x - α ) ( x - ß )

Where k is constant.

⇒ 5x² + 2x - 1 = k ( x² - xß - xα + αß )

⇒ 5x² + 2x - 1 = k { x² - x( α + ß ) + αß }

⇒ 5x² + 2x - 1 = kx² - kx( α + ß ) + kαß

By comparing coefficients ,

⇒ 5x² = kx²

⇒ k = 5x² / x²

∴ k = 5.

And,

⇒ 2x = -kx ( α + ß )

⇒ -k ( α + ß ) = 2x / x

⇒ -k ( α + ß ) = 2

By putting the value of k = 5,

⇒ -5 ( α + ß ) = 2

⇒ ( α + ß ) = 2/ ( -5 )

 ∴ ( α + ß ) = -2/5.


Hope it helps !